Pith. sign in
theorem

primeCoordinateReadoutCommitment_closed

proved
show as:
module
IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.Factorization.GoalClosure
domain
Foundation
line
58 · github
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plain-language theorem explainer

The D4 prime-coordinate readout commitment is discharged: a δ-prime-coordinate transform exists as a nonempty type. Factorization goal-closure work cites this when sealing the residual-closed field of the ledger certificate. The proof is a one-line wrapper around the native-choice existence theorem.

Claim. The D4 prime-coordinate readout commitment holds: the type of $\delta$-prime-coordinate transforms is nonempty (equivalently, such a transform exists).

background

In the Primitive Recognition Calculus factorization layer, the original D4 commitment demands a genuine $\delta$-prime-coordinate transform, not a weaker benchmark or heuristic readout. Formally the commitment is the proposition that DeltaPrimeCoordinateTransform is inhabited.

Upstream, the native-choice construction already supplies one concrete transform and packages nonemptiness as a theorem. This module sits in the GoalClosure ledger: it records that the commitment is closed in the theorem-ledger sense by that native-choice witness, so downstream certificate assembly can treat residual closure as settled.

proof idea

One-line wrapper that applies the upstream theorem establishing nonemptiness of the $\delta$-prime-coordinate transform via the native-choice witness. No extra algebra or case analysis.

why it matters

Feeds the residual-closed field of the goal-closure certificate, which bundles residual naming, transform provenance, exactness, closure, and prime-divisor recovery into one ledger object. Doc-comment: the commitment is closed in the theorem-ledger sense by the native-choice transform. Within Recognition foundation work this seals the D4 readout obligation so factorization residual accounting can proceed without an open commitment hole.

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